I can't figure out how to do the algebra to simplify this expression!
$$w\left(\cfrac Q {1+\frac w r}\right)^2 + r\left(\cfrac Q {1 + \frac r w}\right)^2$$
It's supposed to turn out to $\cfrac {Q^2} {\frac 1 w + \frac 1 r}$. Could someone show the steps on how to get this?
Observe that $\displaystyle\frac a{\left(\dfrac bc\right)}=\frac{ac}b,$ but $\displaystyle\frac {\left(\dfrac ab\right)}c=\frac a{bc}$
Here, $$\frac Q{1+\dfrac wr}=\frac Q{\dfrac{r+w}r}=\frac{Qr}{r+w}$$
$$\implies w\left(\frac Q{1+\dfrac wr}\right)^2=\frac{Q^2r^2w}{(r+w)^2}$$
Similarly, $$r\left(\frac Q{1+\dfrac rw}\right)^2=\frac{Q^2rw^2}{(r+w)^2}$$
Adding we get, $$\frac{Q^2rw^2+Q^2r^2w}{(r+w)^2}=\frac{Q^2rw(r+w)}{(r+w)^2}=\frac{Q^2rw}{(r+w)}$$
Now divide the numerator & the denominator by $rw$
Also, observe that the question itself has assumed that $rw(r+w)\ne0$
